The Regulator Theory for Finite Automata

This paper deals with the problem of controlling the state of a finite automaton to some preassigned value; namely, the regulator problem. First, the simplest situation where the state of the system is currently known is briefly considered and the corresponding solution pointed out. Then, the much more difficult problem arising in the case of nontrivial output transformation is analyzed. This obviously calls for the preliminary solution of the state reconstruction problem in a partially or totally uncertain environment. The obtained results, as compared with the present status of the regulator theory for linear dynamical systems, allow us to point out strong similarities as well as definite differences, the latter being basically due to the essentially nonlinear nature of the systems considered herein.